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Answer :
The first quartile when [tex]\mu = 97.4[/tex] and [tex]\sigma = 17.6[/tex] is [tex]Q_1 = 85.54[/tex] .
In statistics, a quartile is a type of quantile that divides the number of data points into four corridors, or diggings, of more-or-less equal size. The data must be ordered from lowest to largest to cipher quartiles; as similar, quartiles are a form of order statistic.
Let us assume that X is the adult IQ score.
[tex]\mu = 97.4[/tex]
[tex]\sigma = 17.6[/tex]
Let [tex]z_0[/tex] be the z-score for the first quartile.
[tex]P(z\geq z_0 ) = 0.75[/tex]
Now, use the area under the normal curve to find the value of [tex]z_0[/tex] .
[tex]z_0 = -0.674[/tex]
[tex]\frac{X-\mu}{\sigma} = -0.674[/tex]
[tex]\frac{X-97.4}{18.6} = -0.674[/tex]
[tex]X = -0.674\times 18.6 + 97.4[/tex]
[tex]= 85.54[/tex]
Hence, the first quartile is [tex]Q_1 = 85.54[/tex] .
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